Q.3 Suppose that the force acting on a particle is factorable into one of the following...

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Q.3 Suppose that the force acting on a particle is factorable into one of the following forms: (i) F(x, t) = f(xi)g(t), (ii) F(x, t) = f(xi)g(t), (iii) F(x₁, x₁) = f(xi)g(xi). For which cases are the equations of motion integrable and hence correspond to the holonomic constraints? Q.4 Consider a coin rolling without slipping across a horizontal plane such that the plane of the coin remains vertical, but it is free to rotate about the vertical axis. Find out the generalized coordinates required to describe the motion. Write the rolling constraint in differential form. 112 T Q.3 Suppose that the force acting on a particle is factorable into one of the following forms: (i) F(x, t) = f(xi)g(t), (ii) F(x, t) = f(xi)g(t), (iii) F(x₁, x₁) = f(xi)g(xi). For which cases are the equations of motion integrable and hence correspond to the holonomic constraints? Q.4 Consider a coin rolling without slipping across a horizontal plane such that the plane of the coin remains vertical, but it is free to rotate about the vertical axis. Find out the generalized coordinates required to describe the motion. Write the rolling constraint in differential form. 112 T

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